deductive reasoning “the proof is in the pudding.”“indubitably.” je solve le crime. pompt...

Deductive Reasoning

“The proof is in the pudding.”“Indubitably.”Je solve le crime. Pompt de pompt pompt."

Le pompt de pompt le solve de crime!"

2.3 Written Exercises

DB C

A

2.3 Written ExercisesWhat definition, postulate, or theorem justifies the statement about the diagram.

, .If D is themidpt of BC then BD DC

Definition of midpoint

1

43

21

mp

DB C

AWhat definition, postulate, or theorem justifies the statement about the diagram.

Definition of Angle Bisector

2

43

21

1 2 , sec .If then ADis thebi tor of BAC

DB C

AWhat definition, postulate, or theorem justifies the statement about the diagram.

Definition of Angle Bisector

343

21

sec , 1 2.If ADis thebi tor of BAC then

DB C

AWhat definition, postulate, or theorem justifies the statement about the diagram.

4

43

21

03 4 180m m Angle addition postulate

DB C

AWhat definition, postulate, or theorem justifies the statement about the diagram.

5

43

21

Definition of Midpoint

, .If BD DC thenDis themidpt of BC

DB C

AWhat definition, postulate, or theorem justifies the statement about the diagram.

6

43

21

Midpoint Theorem

1, .2

If D is themidpt of BC then BD BC

DB C

AWhat definition, postulate, or theorem justifies the statement about the diagram.

7

43

21

Angle Addition Postulate

1 2m m m BAC

DB C

AWhat definition, postulate, or theorem justifies the statement about the diagram.

8

43

21

Segment Addition Postulate

BD + DC = BC

?80

4018

0 0

9

Write the number that is paired with the angle bisector .CDE

C

E

D

80 40 120 602 2

Average the numbers to find the middle value.

?120

3018

0 010

Write the number that is paired with the angle bisector .CDE

C

E

D

120 30 150 752 2

Average the numbers to find the middle value.

?12218

180 0

11

Write the number that is paired with the angle bisector .CDE

C

E

D

122 18 140 702 2

Average the numbers to find the middle value.

12 A] draw a pair of angles like below.B] measure each angle with a protractor.

60m PMN

P

NL M120m LMP

Note that each number was on the same spot on the protractor.

12

P

NL M

120

C] What is the measure of the angles formed by their bisectors?

60

6030

3060

60 + 30 = 900

12

P

NL M

120

60

6030

3060

D] Explain how you could of known the answer to part C without measuring the angles.

Half of each portion is half of the whole 1800.

13

N

The coordinate of points L and X are 16 and 40 respectively.

N is the midpoint of and Y is the midpoint of LN . Sketch a diagram and find:

LN

L X

16 40

Find LN. LX = 40 – 16 = 24

1 122

LN LX

Y

13

N

The coordinate of points L and X are 16 and 40 respectively.

N is the midpoint of . Sketch a diagram and find:LN

L X

16 40

Find the coordinate of N.

16 40 56 282 2

28Why ?

Average the values.

13

N

The coordinate of points L and X are 16 and 40 respectively.

N is the midpoint of . Sketch a diagram and find:LN

L X

16 40

Find coordinate of Y.

28

Y

22

16 28 44 222 2

13

N

The coordinate of points L and X are 16 and 40 respectively.

N is the midpoint of . Sketch a diagram and find:LN

L X

16 40

Find LY.

28

Y

22

22 – 16 = 6

14

Z

bisects and

bisects and bisects .

Sketch the diagram and find:

SW

RST 72m RST SZ

RSW SR

NSW

m RSZ & m NSZ

W

TS

R 720N

bisects and

bisects and bisects .

14

Z

Sketch the diagram and find:

SW

RST

SZ

RSW SR

NSW

m RSZ & m NSZ

W

TS

R 720N

72m RST

36

36

36

18

18

18

36

15

L

G N H

MK

Suppose that M and N are midpoints of and respectively.Which segments are congruent?

LK GH

LM MK

GN NH

15

L

G N H

MK

What additional information would be needed to conclude ?LK GH

LM GN

16

U V

S R

TSuppose bisects And bisects

What angles are congruent?

SV

RST

RU

SRT

RSV TSV

SRU TRU

16

U V

S R

TWhat additional information would be

needed to show that ?

RSV TSV SRU TRU

VSU URV

RST SRT

17E

A

D

B

C

Given:

What can you deduce from the given information.

AE = DE

CE = BE AC = DB

18E

A

D

B

C

Given:

What can you deduce from the given information.

secAC bi ts DBsecDB bi ts AC

CE = BE AC = DBAE = EC = DE = EB

19

Skip

19 Complete the proof of Theorem 2-2.

Given:

Prove:

is the bisector ofBX ABC

12

m ABX m ABC

BX

is the bisector of ABC

m ABX m XBC

m ABX m XBC m ABC

m ABX m ABX m ABC

2m ABX m ABC

12

m ABX m ABC

GivenDef. of Angle Bisector

Angle Addition PostulateSubstitution

Combine like terms CLT

Division Prop. Of Equality

C’est fini.

Good day and good luck.